Finite-time integral input-to-state stability for switched nonlinear time-delay systems with asynchronous switching

This article is concerned with the stability of switched nonlinear time-delay systems with asynchronous switching. We start by extending the well-known concept of integral input-to-state stability (iISS) to finite-time integral input-to-state stability (FTiISS). It is clear to find that the new concept of FTiISS plays an important role in many branches of engineering and science. Leveraging the Razumikhin-type theorem along with the average dwell time (ADT) and mode-dependent ADT methods, sufficient ISS, iISS, finite-time ISS, and FTiISS criteria for switched nonlinear time-delay systems under asynchronous switching are presented. Our proposed results improve upon the existing results by removing some restrictive conditions, and subsume some existing ones as special cases. Finally, simulation examples are provided to illustrate the effectiveness and advantages of our results.